In a Gaussian optical system, an optical element (e.g., a lens) is considered ideal and free from optical aberration. That is to say, when light generated by a point source of light located in an object space propagates through the optical element in the form of spherical waves, the spherical waves converge into an infinitely small image point (i.e., an ideal convergent wavefront) in a corresponding image space. In reality, an incident wavefront passing through the optical element to an exit pupil, also known as a spherical wavefront, has an optical path difference (OPD) compared with the ideal convergent wavefront, so a convergent wavefront is not able to converge into an infinitely small image point, resulting in a blurred image point and aberration. The OPD may be present due to a number of reasons, such as a non-ideal shape of the optical element attributed to errors in a manufacturing process of the optical element, an error in alignment between two surfaces of the lens, a non-uniform distribution of the optical material, a misalignment error among elements in the optical system, etc. Therefore, in the manufacturing process of the optical element, optical metrology devices such as an interferometer or a wavefront sensor may be employed to evaluate and verify transmitted wavefront of the optical element.
FIG. 1 illustrates a Hartmann-Shack wavefront optical testing system 1 as disclosed in U.S. Pat. No. 6,130,419. The optical testing system 1 includes a light source 11, a null corrector 12, a to-be-tested optical element 13, a collimator 14, a micro-lens array 15, an image sensor 16 and a processing unit 17. The image sensor 16 may include a charge-coupled device (CCD) and/or a complementary metal-oxide-semiconductor (CMOS) sensor (not shown in the drawings). The micro-lens array 15 includes a plurality of lenses 151. The light source 11 generates a uniform light beam that propagates into the null corrector 12, resulting in a corrected wavefront that can be used to compensate the optical aberration, mostly spherical aberration, generated from the to-be tested optical element 13. The corrected wavefront passes through the to-be-tested optical element 13, converges before passing through the collimator 14, and subsequently becomes collimated before entering the micro-lens array 15. The image sensor 16 detects the light projected thereon from the micro-lens array 15, forming at least one image within the range of the light beams. The image includes a plurality of light spots. Specifically, light passing through each of the lenses 151 of the micro-lens array 15 converges into a plurality of light spots, and the irradiance of the light spots may be taken as a wavefront intensity of a light beam from a corresponding one of the lenses 151 of the micro-lens array 15. The processing unit 17 calculates, for each of the light spots, an intensity centroid based on at least one coordinate set and an irradiance of the light spot. One way to calculate the intensity centroid may be employing a center-of-mass algorithm, as described in equation (1) in U.S. Pat. No. 6,130,419. Using the intensity centroid, a displacement of each of the light spots from its ideal position may be obtained precisely. In turn, the displacement of each of the light spots may be used to determine a wavefront slope of the light beam passing through a corresponding lenses 151. The complete wavefront is then reconstructed from the all the local wavefront slopes. The local wavefront phase at the corresponding lenses 151 is then determined. Therefore, by inspecting the irradiance and the displacement of each of the light spots, wavefront information on the corresponding one of the lenses 151 such as a wavefront slope, a wavefront phase and a wavefront intensity may be obtained.
In measuring wavefront aberration of different optical elements, the null corrector 12 and the collimator 14 may need to be customized and manufactured individually, such that when a light beam passes through the null corrector 12, optical aberration complementary to that of the to-be-measured optical element is created to compensate the aberration generated from the to-be-measured optical element.
The unbalanced aberration, specifically, the spherical aberration, in the optical system causes the pupil distortion between the entrance pupil and the exit pupil of the optical system. Since the aberration is balanced between the null corrector 12 and the to-be-tested optical element 13, the pupil distortion is therefore minimized. As a result, the ray distribution of the light beam after passing through the collimator 14 is as uniform as the ray entering the null corrector 12 as shown in the FIG. 1. Additionally, the wavefront intensity distribution of the light beam before arriving at the micro-lens array 15 may be expressed by the graph shown in the FIG. 2, indicating that the intensity distribution is substantially uniform. FIG. 3 illustrates a resulting image detected by the image sensor 16 and including a plurality of light spots having substantially the same spot irradiance.
It is noted that the manufacturing and subsequent alignment of the null corrector 12 and the collimator 14 brings additional costs. Moreover, the null corrector 12 and the collimator 14 themselves may not be fabricated to perfection, and may also have defects that cause transmitted wavefront distortions, reducing the measurement accuracy of the optical testing system 1. It is then desirable that the null corrector 12 and the collimator 14 can be removed from the optical testing system 1 to eliminate the potential issues as described above.
Nonetheless, without the null corrector 12, the aberration contributed from the to-be-tested optical element 13 is not balanced. The resulting pupil distortion causes a difference between the direction of propagation of a light ray located at the periphery of the light beam and that of the light ray located at the center of the light beam. Therefore, the ray distribution of the wavefront entering the micro-lens array 15 is not uniform. As a result, the irradiance of the light spots focused by the micro-lens array 15 is not uniform. Specifically, referring to FIG. 4, in a case that the to-be-tested optical element 13 has, for example, spherical aberration, an intensity of a wavefront entering the micro-lens array 15 may be in the shape of a Gaussian function with a narrower width shown in FIG. 5, indicating that the distribution of the wavefront intensity is not uniform. FIG. 6 illustrates an exemplary resulting image that is detected by the image sensor 16 and that includes a plurality of light spots having widely varying intensities. Specifically, the light spots located in the center of the light beam are considerably much brighter than those located close to the periphery of the light beam. In such a case, calculating the intensity centroid of a either saturated or too dim light spot may yield inaccurate result, therefore, it is nearly impossible to accurately obtain all of the wavefront slopes associated with all of the light spots in a single camera exposure, adversely affecting an accuracy of the wavefront measurement. Therefore, the wavefront measurement of the to-be-tested optical element 13 would fail easily due to the non-uniform light spot distribution.
Therefore, it is desirable to reduce the overall cost for constructing the optical testing system 1 by eliminating the null corrector 12 while overcoming the uniformity problem of the light spot due to the excess optical aberration presenting in the tested light beam.